This is the first paper in a series dealing with the formation of benzene from acetylene on iron clusters, Fe-n/Fe-n(+) (n=1-4). In the present study, we have performed all-electron Kohn-Sham density-functional theory calculations on the adsorption of acetylene and vinylidene on small iron clusters. Many starting structures were fully optimized without geometric and symmetric constraints for at least three different spin states (numbers of unpaired electrons) using gradient corrected functionals. Vibrational analyses have been performed on all the optimized structures. There is a large number of low-lying electronic states within a window of 50 kJ/mol above the lowest-energy structure for each cluster size and charge state. Various types of coordination and numbers of unpaired electrons are encountered in these electronic states. According to our energetic error bar, all of these states are possible candidates for the ground state of a given complex. Inclusion of corrections beyond the gradient of the density in generalized gradient approximation functionals for correlation stabilizes electronic states with high magnetic moment and destabilizes the low spin states. Electronic states corresponding to the adsorption of an acetylene or a vinylidene molecule on only one iron atom are also more stable when higher corrections are included in the correlation functional. Finally, we have excluded the participation of the vinylidene molecule in the reaction mechanism of the formation of benzene from acetylene on small iron clusters. (C) 2003 American Institute of Physics.